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We study the equivariant elliptic characteristic classes of Schubert
varieties of the generalized full flag variety $G/B$. For this first we need to
twist the notion of elliptic characteristic class of Borisov-Libgober by a line
bundle, and thus allow the elliptic classes to depend on extra variables. Using
the Bott-Samelson resolution of Schubert varieties we prove a BGG-type
recursion for the elliptic classes, and study the Hecke algebra of our elliptic
BGG operators. For $G=GL_n(C)$ we find representatives of the elliptic classes
of Schubert varieties in natural presentations of the K theory ring of $G/B$,
and identify them with the Tarasov-Varchenko weight function (a.k.a. elliptic
stable envelopes for $T^*G/B$). As a byproduct we find another recursion,
different from the known R-matrix recursion for the fixed point restrictions of
weight functions. On the other hand the R-matrix recursion generalizes for
arbitrary reductive group $G$.查看全文